Real-Time Regulation-Aware Game-Theoretic Motion Planning for Head-to-Head Autonomous Racing

This paper presents the real-time implementation and experimental validation of a regulation-aware, game-theoretic motion planning framework for autonomous racing. The framework builds on a Regulation-Compliant Model Predictive Control (RC-MPC) formulation that encodes overtaking rules using the Mixed Logical Dynamical (MLD) framework. Interactions among vehicles are modeled as a Generalized Nash Equilibrium Problem (GNEP) and solved by the Regulation-Aware Game-Theoretic Planner (RA-GTP). The main contributions of this paper are: (i) a tailored Real-Time Iteration (RTI) scheme within a Mixed-Integer Sequential Quadratic Programming (MISQP) solver for regulation-compliant MPC, (ii) a single-pass Iterated Best Response (IBR) method enabling real-time game-theoretic reasoning, and (iii) the first experimental validation of regulation-aware planning on the 1:10-scale Berkeley Autonomous Race Car (BARC) platform in competitive head-to-head racing. To reduce the number of binary variables and further lower the computational complexity of the problem, part of the regulation logic is pre-computed. Experimental results demonstrate that the proposed planner computes feasible, regulation-compliant trajectories in real time, achieving competitive and strategic overtakes, as opposed to a regulation-agnostic baseline that proves overly conservative.